Converting Fractions to Decimals and Order of Operations

 

  1. Converting Fractions to Decimals

    To convert fractions to decimals we just divide.  The only catch is when should we stop.  Sometimes we end when there is no remainder.


    Example

    Convert the fraction 3/8 to a decimal.

    Solution

                 0.375
            8 | 3
    .000  
                 24        
                   60       
                   56   
                     40   
                     40
                       0

    Hence    

                 3
                       =  0.375                 
                 8

    Other times the digit repeats itself

    Example

    Convert the fraction 5/6 to a decimal.


    Solution

                 0.833
            6 | 5
    .000  
                 48        
                   20       
                   18   
                     20   
                     18
                       20

    We see that if we keep working it out we will continually get 3.  That is 
        

                 5
                       =  0.833333...                 
                 6

    We put a bar over the 3 to indicate that the 3 repeats.

    0.83333...  =  0.83 


    Example

    Convert the fraction 4 2/7 to a decimal.


    Solution

    Divide only the fractional part

                 0.285714
            7 | 2
    .00000000  
                 14        
                   60       
                   56   
                     40   
                     35
                       50
                       49
                         10
                           7
                           30
                           28
                             20       
    We are back to where we began.


    Hence 
        

                   2
             4          = 
    .285714Notice the 4 from the mixed number is the whole number part.             
                   7


    Example

    Fill in the green blank with "<" , ">", or "="

               2
                    
                       0.133
              15           


    Solution

    We first convert the fraction into a decimal.  Then compare.  We will need to divide until we recognize a difference or recognize equality

                  0.13
            15 | 2
    .00  
                   15        
                     50       
                     45   
                        50   

    We see that this is the repeating decimal 

            0.13   =  0.133333... 

    Now notice that 

            0.133 = 0.133000000... < 0.1333333...



    Exercises

    Convert the following fractions to decimals

    1. 3/4        0.75

    2. 8 5/9        8.5 Bar over the 5

    3. 7  2/11        7.18  Bar over the 18

     

  2. Order of Operations

    Just as with whole numbers and fractions the order of operations is:

    1. Inside parentheses
    2. Exponents
    3. Multiplication and Division    For a tie go left first
    4. Addition and Subtraction        For a tie go left first

    Example

    Calculate

            (2.1 - 1)2 + 5.6 x 4

    Solution

            (2.1 - 1)2 + 5.6 x 4

            =  (
    1.1)2 + 5.6 x 4

            = 
    1.21 + 5.6 x 4        (1.1)2  =  1.1 x 1.1  =  1.21

           
    =  1.21 + 22.4        5.6 x 4  =  22.4

         
       =  23.61

    Exercise

    Calculate

           
    (5 - 2.3) 0.12 + 3.2 x 0.5     271.6


  3. Application

    Your drill bit is 3/16 inches in radius, but the screw that is to go into the hole is supposed to be 0.2 inches in radius.  How much bigger is the screw then the hole?

    Solution

    We convert 3/16 to a decimal.

                   0.1875
            16 | 3
    .0000     
                   16        
                    140       
                    128   
                      120  
                      112
                          80
                          80
                            0

    Finding how much bigger is a subtraction problem

                 
    199
              0.200
    10
          -   0.1875
               0.0125

    The radius of the screw is 0.0125 inches bigger than the radius of the hole.

 



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